Question

A 0.1 significance level is used for a hypothesis test of the claim that when parents use a particular method of gender​ selection, the proportion of baby girls is greater than 0.5. Assume that sample data consists of 66 girls in 121 ​births, so the sample statistic of six elevenths results in a z score that is 1 standard deviation above 0. Complete parts​ (a) through​ (h) below. Identify the null hypothesis and the alternative hypothesis. What is the value of a? What is the sampling distribution of the sample​ statistic? Is the test​ two-tailed, left-tailed, or​ right-tailed? What is the value of the test​ statistic? What is the​ P-value? What are the critical​ value(s)? What is the area of the critical​ region?

Answer 1

Ans:

level of significance=0.1

sampling distribution of sample proportion:

mean=0.5

standard deviation=sqrt(0.5*(1-0.5)/121)=0.0455

sample proportion=66/121=0.5455

right tailed

Test statistic:

z=(0.5455-0.5)/0.0455

z=1

p-value=P(z>1)=0.1587

critical z value=1.282

area of critical region=0.1

Fail to reject the null hypothesis.